Answer:
3. x = - 2, 4. x = 1-----------------------------
Question 3Given equation:
x + 4 = - xIn order to solve it by graphing, plot two lines:
y = x + 4 and y = - xThe solution is the x-coordinate of the intersection of the lines:
x = - 2See the attached
Question 4Given equation:
-2x + 6 = 5x - 1Similar to the previous question, plot the lines and take the x-coordinate of the intersection as solution.
y = - 2x + 6 and y = 5x - 1The solution is x = 1.
See the attached.
X≠? F(x)=sin(2x/(1+sin(2x))
Step-by-step explanation:
a/b is invalid, when b = 0.
so, F(x) is invalid, if (1 + sin(2x)) = 0.
(1 + sin(2x)) can only be 0, if sin(2x) = -1
sin(angle) = -1
angle = 2x = 270° or 3pi/2
x = 135° or 3pi/4
so,
x <> 135° or 3pi/4
The great pyramid has base length b = 233 meters and height h = 147 meters. Assume one side of this pyramid can be represented by a triangle formed by points depicted in the following diagram. Find the area (in square meters) of one side (shaded green in the diagram).
The area of the triangular side of the pyramid is given as follows:
21,852 m².
How to obtain the area of the side of the pyramid?We consider that the side of the pyramid is triangular, hence we must consider that the area of a triangle is obtained as half the multiplication of the base by the height, that is:
Area = base x height / 2.
Considering b = 233, and dividing by the square root of 2, the coordinates of the endpoints of the base are given as follows:
(164.76, 0, 0) and (0, 164.76, 0).
Hence the length of the base is obtained using the distance between two points as follows:
Base = [tex]\sqrt{164.76^2 + 164.76^2}[/tex]
Base = 233.
The midpoint of the base has the coordinates given as follows:
(82.38, 82.38, 0).
The height is the distance between (0,0,147) and (82.38, 82.38, 0), hence it is given as follows:
Height = [tex]\sqrt{82.38^2 + 82.38^2 + 147^2}[/tex]
Height = 187.57.
Hence the area is of:
Area = 0.5 x 233 x 187.57
Area = 21,852 m².
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3. George intends to drive from Atlanta to Chicago, a distance of 710
miles. He drives at an average rate of 46 miles per hour for the first 5
hours. What is his average driving rate for the remainder of the trip if
the entire trip takes 12.5 hours?
Answer:
64 mph
Step-by-step explanation:
46 x 5 = 230
710 - 230 = 480 is the distance that he has left
distance = rate x times
480 = rate x 7.5 (12.5 -5 = 7.5)
480 = r(7.5) Divide both sides b y 7.5 to find the rate
480/7.5 = [ r(7.5) ]/7.5
64 = r
G(x)=-f(x)+10 and h(x)=-f(x-4)+10 functions g and h differ
The difference between the functions G(x) and h(x) is 4 units.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The functions are given in the question, as follows:
G(x)=-f(x)+10 and h(x)=-f(x-4)+10
Since the functions, g and h differ
This can be seen by subtracting G(x) from h(x):
h(x) - G(x) = (-f(x-4) + 10) - (-f(x) + 10)
h(x) - G(x) = 4.
This means that for any value of x, the output of h(x) will be 4 units greater than the output of G(x).
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The population of a city decreases by 1% per year. If this year's population is 238,000, what will next year's population be, to the nearest individual?
The nearest person is 235620 populations away in the following year.
The rate of decrease of a populationThe country, territory, or geographic area's yearly average rate of change in population size over a certain time period.
From the given question, we have the following:
Total population this year = 238,000 population
If the population of a city decreases by 1% per year, the population next year will be 99% of the current population to have:
Population this year = 99% of 238,000 population
Population this year = 0.99 * 238,000
Population this year = 235620 populations
Hence the next year's population to the nearest individual is 235620 populations
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find square root of 10609
Answer:
103
Step-by-step explanation:
because its the actual answer
Write and solve an inequality.
The speed limit of a highway is 65 miles per hour. A car is traveling at least 74 miles per hour. How many miles per hour, m, over the speed limit is the car traveling?
Answer:
The car is travelling at least 9 mph over the speed limit---------------------------
The speed limit is 65 mph, the speed of the car is at least 74 mph.
The difference m is the over the speed limit value.
Set an inequality:
65 + m ≥ 74m ≥ 74 - 65m ≥ 9А
5 m/s
2 m/s
A-B = ?
The correct answer is C. You've got that right.
A pole that is 2.5 m tall cast a shadow that is 1.63 m long. At the same time, a nearby building cast a shadow that is 35.75 m long. How tall is the building?
Answer:
The building is 36.62 m long.
Step-by-step explanation:
The difference between the pole and its shadow》2.5m - 1.63m = 0.87m {So the shadow pole is 0.87m shorter than the actual pole }So if the shadow of the building is 35.75m....then the actual building should be 0.87m longer than it, therefore 》35.75m + 0.87m = 36.62 mFind the mode for the following set of data78,60,54,76,64,56,62,67
Answer:
There is no mode for this set of numbers.
Step-by-step explanation:
The mode is the value that appears most frequently in a data set.
54,56,60,62,64,67,76,78
In this set of numbers no value appears more than once.
This means there is no mode for this set of data.
o
Which people's scores on the bar chart do not match the data given in the table?
Geography vs History test scores
Bookwork code: E40
Samuel
12
Isabella 18
7
19
10
Bradley
Phoebe
Charles
Geography History
test score test score
Calculator
not allowed
14
15
9
13
6
20 15 10 5 0
Geography test score
Samuel
Isabella-
Bradley
Phoebe
Charles
0
5 10 15
History test score
20
The people whose scores on the bar chart do not match the data given in the table are Georgia and Eleanor.
What is a bar chart?In Mathematics, a bar chart (bar graph) simply refers to a type of chart that is used for the graphical representation of a population (data set), especially through the use of rectangular bars and vertical columns.
Based on the given bar chart which represents people's test scores in English and French, we can reasonably infer and logically deduce that table showed that Eleanor scored 12 in her English test while it was recorded as 14 on the bar chart.
Similarly, the table showed that Georgia scored 18 in her English test while it was recorded as 15 on the bar chart.
In conclusion, both Georgia and Eleanor were not correctly recorded on the bar chart.
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A book Thandi is reading features totem poles from two regions in the Pacific Northwest.
The two-way table shows some of the animals carved in the totem poles and the regions where the totem poles are located.
Thandi states that 20% of Alaskan totem poles featured in the book have eagles carved in them. Use the drop-down menus to explain and correct Thandì's error.
Answer:
Step-by-step explanation:
Thandi's statement that 20% of Alaskan totem poles featured in the book have eagles carved in them is not accurate.
A two-way table, also known as a contingency table, is used to organize and display the relationship between two categorical variables. The table shows the frequency or count of observations for each combination of the two variables. In this case, the two variables are the animals carved in the totem poles and the regions where the totem poles are located.
To find the percentage of Alaskan totem poles that have eagles carved in them, we need to divide the number of Alaskan totem poles with eagles by the total number of Alaskan totem poles and multiply by 100. This can be calculated as:
(Number of Alaskan totem poles with eagles / Total number of Alaskan totem poles) * 100
Without the data for the two-way table it's impossible to check if the statement is correct or not. It's important to note that without the data it is also impossible to know the context of the statement and the information provided in the book.
Answer:
=Have Eagles
=50%
Step-by-step explanation:
Thandi may have found the percent of the total totem poles that have eagles. The actual percent of Alaskan totem poles that have eagles carved in them is 50%.
Which of the following gives a single solution of the inequality Ix+3I-2 greater than or equal to 0 and shows a graph that can be used to determine the entire solution set of the inequality?
The solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
|x + 3| - 2 ≥ 0
⇒ |x + 3| ≥ 2
Using: If |u| ≥ a, a > 0 then u ≤ -a, u ≥ a
⇒ x + 3 ≤ -2, x + 3 ≥ 2
x ≤ -5, x ≥ -1
Hence, the solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).
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f(x) = x-4 / x^2 +13x + 36
Answer:
Step-by-step explanation:
This is a quadratic function, which is a function of the form f(x) = ax^2 + bx + c, where a, b and c are constants. The function can be written in general form as f(x) = (x-4) / (x^2 +13x + 36).
To find the roots of the function (i.e. the points at which the function intersects the x-axis), we can use the quadratic formula:
x = [-b +/- sqrt(b^2 - 4ac)] / 2a
In this case, a = 1, b = 13 and c = 36.
Substituting these values into the quadratic formula, we get:
x = [-13 +/- sqrt(169 - 4(1)(36))] / 2
x = [-13 +/- sqrt(97)] / 2
x = [-13 +/- 9.8488578] / 2
x1 = -1.1744289
x2 = 11.1744289
Therefore, the roots of the function are x1 = -1.1744289 and x2 = 11.1744289.
In 25 years, a bond that paid 7.75% simple interest earned $3,875 interest. What was the principal of the bond in dollars?
Answer:
The principal of the bond can be calculated using the formula Principal = Interest / Rate x Time. In this case, the interest is $3,875, the rate is 7.75%, and the time is 25 years. Therefore, the principal of the bond is: Principal = $3,875 / 0.0775 x 25 = $20,000.
Step-by-step explanation:
The principal of the bond can be calculated using the formula Principal = Interest / (Rate x Time), where Interest, Rate and Time are given in the problem statement.
By using this formula, the principal of the bond is $20,000. This is the amount of money that was invested to earn the interest of $3,875 over 25 years with the interest rate of 7.75%.
Find a formula for the described function. A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides. State the domain of A
The domain of the area of the given rectangle is; 0 < A < 1
How to change the subject of the formula?The subject of a formula is defined as the variable that is being worked out. This subject of formula can be easily recognized as the letter that is on its own on one side of the equals sign. For example, in the formula for the area of a rectangle A = bh, the subject of the formula is A.
Now, we are told that the rectangle has perimeter of 8 m.
The formula for the perimeter of a rectangle is;
P = 2(L + W)
We are told that the perimeter is 8 m. Thus;
2(L + W) = 8
L + W = 4
W = 4 - L
Formula for area of a rectangle is;
A = LW
Thus;
A = L(4 - L)
A = 4L - 4L²
At A = 0, we have L = 0 OR 1
The value of A cannot be zero or 1 and as such the domain of A is the;
0 < A < 1
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If P(D) = 0.26 and P(R) = 0.38, what is P(D or R) if D and R are independent?
If D and R are independent, then P(D or R) = 0.8412
What are independent events?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)
P(D) = 0.26 and P( R) = 0.26 , if D and R are independent, then,
P(D or R) = P(D) + P(R) - P(DnR)
then P(DnR) = P(D) × P(R) = 0.26×0.38 = 0.0988
P(D or R) = 0.26+0.38-0.0988
= 0.8412
Therefore the probability of P(D or R) if D and R are independent is 0.8412
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how many times does 11 go into 40
The required, 11 goes into 40 three times with a remainder of 7.
What is simplification?Simplification involves applying rules of arithmetic and algebra to extract undeserved terms, factors, or processes from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property
11 goes into 40 three times with a remainder of 7.
We can use long division to find the answer:
3
11 | 40
33
---
7
Therefore, 11 goes into 40 three times with a remainder of 7.
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Will, I get my answers right away?
PLEASE IF U GET THE ANSWER SHOW UR WORK write the equation for the line that passes through the given point, and is parallel to the given line.
(-3,-1); x-2y = 5
Answer:
y = 5x - 4
Step-by-step explanation:
1. Parallel have the same slope (equation)
- Standard form of an equation of a line: y=mx + b
m = slope
x = x-coordinate
b = y-intercept
y = y-coordinate
SLOPE = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]
Given that x-2y = 5
and the line has the point:
(-3,-1)
We need to find another point to find the slope
x - 2y = 5
Let's say x = 7 and y = 1
(7, 1)
Now plug it into the slope equation
[tex]\frac{-3-7}{-1-1} = \frac{-10}{-2} = 5[/tex]
Plug the slope into the standard form of an equation of a line
y = 5x + b
Plug in (7,1)
1 = 5 + b
b = -4
The answer is: y = 5x - 4
Hope this helps :)
Have a great day!
give me a sum using all bodmas operations that equals 6
The BODMAS acronym is for:
Brackets (parts of a calculation inside brackets always come first).Orders (numbers involving powers or square roots).Division.Multiplication.Addition.Subtraction.Addition and Subtraction
The final step is to calculate any addition or subtraction. Again, subtraction and addition rank equally, and you simply work from left to right.
Example:
⇒4 + 6 − 7 + 3 = ?
You start on the left and work your way across.
⇒4 + 6 = 10
⇒10 − 7 = 3
⇒3 + 3 = 6
The answer is 6.
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Find the vertex, focus and directrix of the parabola
Y=1/6(x²-8x+6)
Vertex: (4,1/6) Focus: (4,7/12) Directrix: x=2
Which two segments are congruent?
A) RS and XP
B) CS and XP
C) RT and SP
D) CA and RY
In the given question, the segments which are congruent are:-
RS and XP
What is congruent in math?Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
What is a congruent example?Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.
In the gievn figure
the length and size of RS and XP segments are equal
Hence they are congruent
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Please what is the right answer?
well, more often than not we arrange a polynomial in a descending order per degree of term, now, depends on the operation needed for it, we do or we don't, but more often we do.
the assumption in the material is that there are some missing terms in the desscending order. Check the picture below.
Please help due tonight
A monument is 315 feet tall.
Suppose a 12-foot-tall pole that
is near the monument casts a
5-foot shadow.
How long
is the
monuments
shadow?
Answer:
131.25 feet.
Step-by-step explanation:
We can use the concept of similar triangles to find the length of the monument's shadow.
Since the pole and the monument are casting the shadows, we can assume that the ratio of the height of the pole to the length of its shadow is equal to the ratio of the height of the monument to the length of its shadow.
12/5 = 315/x
Where x is the length of the monument's shadow.
We can cross-multiply and solve for x:
12x = 5315
x = 5*315/12
x = 131.25
So, the length of the monument's shadow is approximately 131.25 feet.
2 1/5 of the quotient of 5 5/11 and 2 2/5
Please help me!
Answer:
21 and 18.48 respectively
Step-by-step explanation:
to solve this question,first we need to identify the quotients by dividing the numbers and multiply each by 21/5
The quotient of the [tex]\frac{55}{11}[/tex]=5
[tex]\frac{21}{5}[/tex] of 5 = [tex]\frac{21}{5}[/tex]×5=21
The quotient of the [tex]\frac{22}{5}[/tex]=4.4
[tex]\frac{21}{5}[/tex] of 4.4 = [tex]\frac{21}{5}[/tex]×4.4=18.4
so, the answer is 21 and 4.4 respectively.
Raquel trabaja en un banco. El banco en el que trabaja Raquel recibió una previsión de 1 024 monedas de 10 centavos. Cada rollo de monedas de 10 centavos contiene 8 monedas. ¿Cuántos rollos de 10 centavos recibió e banco?
Answer:
El banco recibió 128 rollos de monedas de 10 centavos.
Step-by-step explanation:
Para saber cuantos rollos de monedas de 10 centavos recibió el banco, podemos dividir el total de monedas recibido entre el número de monedas por rollo.
(1 024 monedas) / (8 monedas/rollo) = (x rollos)
Donde x es el número de rollos recibido. Para calcular x se divide 1 024 entre 8
x = 1 024 / 8
x = 128
Which of these choices show a pair of equivalent expressions? Check all that apply
So, on solving the provided question we can say that [tex]24\sqrt{ 75/7}[/tex] and [tex]\sqrt{67/2 }[/tex] these both are are radials from the given expressions
what are radicals?A radical is a symbol for the square root or nth root. Root expressions are those that contain square roots. A number or word that appears there is a radical's radicand. Examples are the radicals 7 and 2y+1. Radicals can also be characterized by the following terms: Equations containing radicals are referred to as radical equations. The expression found inside the square root is known as a "root expression." The digits 2, 372, 2x+7, and 41p serve as illustrations of radical representations.The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
[tex]24\sqrt{ 75/7}[/tex] and [tex]\sqrt{67/2 }[/tex] here,
these both are are radials from the given expressions
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Simplify the following.
The value of the expression is (x∧2m-15)Yy∧5n +1). Option B
How to simplify the expression?You should understand that simplification involves making an expression more simpler to understand. Also, the expression is in index form that involves the division law of indices.
the given expression to be simplified is
(x∧3m-8)/x∧m-7) (y∧7n +1)/(y∧2n)
This can be simplifies as follows
(x∧3m-8-(m-7)(y∧7n+1(2n)
Simplify further to have the value
(x∧3n-8-m-7)(y∧7m-2n+1)
This implies that the value is
(∧2m-15)(y2n+1)
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Every 10 seconds in escalator step rise is 6 feet
a)
Think of this as a graph
Time (x)-10-20-30-40
Distance escalator rises (feet)
b) Draw a graph to represent the situation. All axis must be properly labeled using appropriate skills that at least four data points fit on the graph c) what is the slope line
d) interpret the unit rate
e) what is the equation of the line
The equation y = 0.60x. The 0.60 represents the 0.60 feet in each second rise. The table is completed below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Every 10 seconds in the escalator step rise is 6 feet.
Let 'y' be the number of feet and 'x' be the number of seconds. Then the equation is given as,
y = 0.60x
Then the table is given as,
Time (x) Distance escalator rises (feet)
10 6
20 12
30 18
40 24
The 0.60 represents the 0.60 feet in each second rise.
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